Question: Rewrite as a simplified fraction. ${3.8\overline{3} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 383.3333...\\ 10x &= 38.3333...\end{align*}}$ Subtracting the two equations, we have: ${90x = 345}$ ${x = \dfrac{345}{90}} $ ${x = \dfrac{23}{6}} \text{or} {3 \dfrac{5}{6}}$